This section is intended to introduce the reader to various aspects of art, which may be related to various aspects of the present principles that are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present principles. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.
The feature points of a surface mesh, wherein a 3D object is represented by such mesh, are defined as the locations where the parameters of a fitted local model (referred to as the “signature”) reach some extreme values (or more generally are close to some specific values). In other words, by locally fitting a parametric model on the surface, one can establish a mapping from the spatial domain (surface of the object in 3) to the parameter space (whose dimension equates the number of parameters in the model), where the feature points are located in a subspace of the parameter space. Popular parametric models include quadric models (sphere, paraboloid, ellipsoid . . . ), and more complex ones.
In the context of surface mesh watermarking, feature points are usually introduced as landmarks to create a canonical partitioning of the mesh prior to watermark insertion/extraction as disclosed for instance in P. Rondao-Alface and B. Macq in “Blind watermarking of 3D meshes using robust feature points detection” (IEEE International Conference on Image Processing, 2005). They disclosed a method that is advantageously robust against cropping since the payload is repeatedly embedded in each element of the partition. However defining a cropping-invariant partitioning mechanism for 3D meshes represents a complex task. Besides the location of these landmarks is content-dependent and usually relies on umbilical points or mesh prongs, i.e. feature points that are uncontrollable and noticeable. In other words, the location of the feature points is public knowledge and an adversary could target the attacks on these very points of the mesh.
In “Digital watermarking of 3D meshes” (Proceedings of SPIE Vol. 5208), Barni et al. disclose a blind watermarking algorithm for 3D meshes. Watermarking is achieved by perturbing the position of the vertices of a low resolution version of the mesh according to a spherical pseudo-random bumped surface. The pseudo-random position and amplitude of the bumps encode the watermark. However, at the detection, the technique of Barni raises the issue of synchronizing the spherical pseudo-random bumped surface with the low resolution model.
In “A Comprehensive Survey on Three-Dimensional Mesh Watermarking” (in IEEE TRANSACTIONS ON MULTIMEDIA, December 2008) Wang et al. presents a comprehensive survey on 3-D mesh watermarking covering an introduction to the relevant state of the art, an attack-centric investigation, and a list of existing problems and potential solutions. First the survey at most discloses perspective in the domain of watermarking with shape descriptor and secondly the survey fails to disclose a 3D-watermarking method on based on arbitrarily-chosen vertices.
Thus a method for watermarking a 3D object based on arbitrarily-chosen vertices is therefore needed. To preserve the quality of the 3D object, these watermarked points should also be imperceptible.